Raimund Bürger, Christophe Chalons, Luis M. Villada:
On second-order antidiffusive Lagrangian-remap schemes for multispecies kinematic flow models
This paper focuses on the numerical approximation of the solutions of multi-species kinematic flow models. These models are strongly coupled nonlinear first-order conservation laws with various applications like sedimentation of a polydisperse suspension in a viscous fluid, or traffic flow modeling. Since the eigenvalues and eigenvectors of the corresponding flux Jacobian matrix have no closed algebraic form, this is a challenging issue. A new class of simple schemes based on a Lagrangian-Eulerian decomposition (the so-called Lagrangian-remap (LR) schemes) was recently advanced in [R. Bürger, C. Chalons, L.M. Villada, SIAM J. Sci. Comput. 35 (2013) B1341-B1368] for traffic flow models with nonnegative velocities, and extended to models of polydisperse sedimentation in [R. Bürger, C. Chalons, L.M. Villada; submitted (2015)]. These schemes are supported by a partial numerical analysis when one species is considered only, and turned out to be competitive in both accuracy and efficiency with several existing schemes. Since they are only first-order accurate, it is the purpose of this contribution to propose an extension to second-order accuracy using quite standard MUSCL and Runge-Kutta techniques. Numerical illustrations are proposed for both applications and involving eleven species (sedimentation) and nine species (traffic) respectively.
This preprint gave rise to the following definitive publication(s):
Raimund BüRGER, Christophe CHALONS, Luis M. VILLADA: On second-order antidiffusive Lagrangian-remap schemes for multispecies kinematic flow models. Bulletin of the Brazilian Mathematical Society, (New Series), vol. 47, 1, pp. 187-200, (2016).